The module will comprise lectures and at least two taught lab sessions. The lecture notes will be provided on-line below both in PDF format and read-only pptx files with audio. The lab sessions will introduce the basic Fortran programming skills required for the module. By the end of the lab sessions each student will have written their own Monte Carlo codes to sample from probability distribution functions and also a code that simulates isotropic scattering of radiation from a point source at the centre of a unifom density sphere. Another lab session will follow on from lectures that describe a publicly available three dimensional scattering code. During this lab session, students will be led through the 3D code's subroutines and how to adapt them for their own three dimensional radiation transport simulations.

**Prerequsites:** PH2012: Physics 2B, plus at least 1 of the following:
AS3013: Computational Astrophysics, PH3080: Computational Physics,
PH3081: Mathematics for Physicists, PH3082: Mathematics for Chemistry/Physics

Steve Jacques (who gave three guest lectures in 2014) has supplied this review chapter on Monte Carlo simulations of photon transport in biological tissue: PDF

Lecture 1: Overview and background requirements PDF

Lecture 2: Introduction and history PDF

Lecture 3: A Monte Carlo Scattering Code: Part 1 PDF

Lecture 4: A Monte Carlo Scattering Code: Part 2 PDF

Lecture 5: Intensity moments, Monte Carlo estimators, random numbers PDF

Lecture 6: Monte Carlo sampling techniques PDF

Lecture 7: Variance reduction techniques PDF

Lecture 8: Neutron transport: revision & outline of MCRT ideas PDF

Lecture 9: Monte Carlo neutron transport & criticality calculations PDF

Lecture 10: Scattering and refractive index changes PDF

Lecture 11: MCRT on a 3D Cartesin Grid PDF

Lecture 12: Monte Carlo photoionization PDF

Lecture 13: Time dependent MCRT and radiation magneto hydrodynamics PDF

Guest lectures will not be given in 2021, but PDFs available here:

Louise Campbell (2016): Monte Carlo simulations of photodynamic therapy PDF

Prof Jerry DeGroot from St Andrews School of History has kindly provided these two articles that you may be interested in reading before the history lectures and morality discussion session.

Jerry's lecture to the Royal United Service Institute

Jerry DeGroot: Physics and morals I PDF

Jerry DeGroot: Physics and morals II PDF

In around week 7, there will be a lab session on using my 3D grid code. The Lab script for the 3D grid code is here: PDF

This lecture closely follows the Stanford tutorial linked below.

You may wish to use the random number generator ran2.f from Numerical Recipes for the exmple sheet problems. For the example in my fortran notes to numerically integrate the solar spectrum, read in the fluxes and wavelengths from this file: solarspectrum.dat.

Fortran 90 Computational Astrophysics taught by Peter Woitke at St Andrews

Fortran 77 tutorial from Stanford University

Fortran notes from the University of Hawaii

The code writes out a file "density.dat" which is an unformatted fortran file comprising the 3D density grid. You may use this short fortran code, read_write.f to read in the density grid and write out a 2D slice through the grid. You can then import the output 2D slice into a plotting program (gnuplot, IDL, Mathematica, etc) to display the slice as a 2D image.

**Texts, Notes, and Review Chapters:**

The classic text by Cashwell and Everett (1957): A Practical Manual on the
Monte Carlo Method for Random Walk Problems
PDF

Monte Carlo Techniques of Electron and Photon Transport for Radiation
Dosimetry by Rogers and Bielajew PDF

**Historical development of Monte Carlo Radiation Transfer**

The following files are from the Los Alamos archive and give a very
enjoyable overview of the development of MCRT.

Letter from John von Neumann to Bob
Richtmyer, 1947

The Beginning of the Monte Carlo Method
by Nick Metropolis

Stan Ulam, John von Neumann, and the Monte
Carlo Method, by Roger Eckhardt

Metroplois, Monte Carlo, and the MANIAC, by
H.L. Anderson

**Lecture Courses and Summer Schools**

St Andrews Monte Carlo Summer School